What is the Greatest Common Factor of 20900 and 20919?

Greatest common factor (GCF) of 20900 and 20919 is 19.

GCF(20900,20919) = 19

We will now calculate the prime factors of 20900 and 20919, than find the greatest common factor (greatest common divisor (gcd)) of the numbers by matching the biggest common factor of 20900 and 20919.

How to find the GCF of 20900 and 20919?

We will first find the prime factorization of 20900 and 20919. After we will calculate the factors of 20900 and 20919 and find the biggest common factor number .

Step-1: Prime Factorization of 20900

Prime factors of 20900 are 2, 5, 11, 19. Prime factorization of 20900 in exponential form is:

20900 = 2² × 5² × 11¹ × 19¹

Step-2: Prime Factorization of 20919

Prime factors of 20919 are 3, 19, 367. Prime factorization of 20919 in exponential form is:

20919 = 3¹ × 19¹ × 367¹

Step-3: Factors of 20900

List of positive integer factors of 20900 that divides 20900 without a remainder.

1, 2, 4, 5, 10, 11, 19, 20, 22, 25, 38, 44, 50, 55, 76, 95, 100, 110, 190, 209, 220, 275, 380, 418, 475, 550, 836, 950, 1045, 1100, 1900, 2090, 4180, 5225, 10450

Step-4: Factors of 20919

List of positive integer factors of 20919 that divides 20900 without a remainder.

1, 3, 19, 57, 367, 1101, 6973

Final Step: Biggest Common Factor Number

We found the factors and prime factorization of 20900 and 20919. The biggest common factor number is the GCF number.
So the greatest common factor 20900 and 20919 is 19.

Also check out the Least Common Multiple of 20900 and 20919